1. I want students to know what a number is (ANYTHING that you can add, subtract, multiply or divide).
2. I want students to know that mathematics is used to make predictions, and I want them to be able to use mathematics to make predictions.
3. I want students to understand how new math is created.
I think I’ve got a shot at hitting 1 and 2 in my classroom, but I haven’t even tried to hit 3.
I want students to understand that math is not just plugging numbers into equations or finding out how quickly trains move, but that it is also a logical thought process that can carry over into any situation. In mathematics, as in life, there are several pathways to yield a similar result. Also, in mathematics, as in life, some pathways are more logical than others. Being able to think about and see where you want to get often allows us to make those logical choices and not go down dead paths.
Also, being able to see a big problem and break it down into the small chunks that it really is, is an important skill. This (magically) also applies to life and problems that people encounter on a day to day basis.
Yes, I want them to see the beauty that mathematics brings to the world, but I also want them to realize that math is just a logical progression of thought and that part of it (sometimes more than other parts of math) can be applied to life almost instantly.
Building our Classroom 
1. I want students to know what a number is (ANYTHING that you can add, subtract, multiply or divide).
2. I want students to know that mathematics is used to make predictions, and I want them to be able to use mathematics to make predictions.
3. I want students to understand how new math is created.
I think I’ve got a shot at hitting 1 and 2 in my classroom, but I haven’t even tried to hit 3.
I want students to understand that math is not just plugging numbers into equations or finding out how quickly trains move, but that it is also a logical thought process that can carry over into any situation. In mathematics, as in life, there are several pathways to yield a similar result. Also, in mathematics, as in life, some pathways are more logical than others. Being able to think about and see where you want to get often allows us to make those logical choices and not go down dead paths.
Also, being able to see a big problem and break it down into the small chunks that it really is, is an important skill. This (magically) also applies to life and problems that people encounter on a day to day basis.
Yes, I want them to see the beauty that mathematics brings to the world, but I also want them to realize that math is just a logical progression of thought and that part of it (sometimes more than other parts of math) can be applied to life almost instantly.